Noncoherent Ultra Wideband Wireless Sensor
Networks for Primary User Detection
Ya˘gmur Sabucu
Faculty of Electrical and Electronics Engineering Bo˘gazic¸i University
Istanbul, Turkey, Email: sabucu@itu.edu.tr
Serhat Erk¨uc¸¨uk
Faculty of Engineering and Natural Sciences Kadir Has University
Istanbul, Turkey Email: serkucuk@khas.edu.tr
Abstract—As a result of increasing demand for new technolo-gies, unlicensed usage of available spectrum has become very essential to provide an efficient usage of spectrum. For that reason, sensor networks may be a reliable option to decide on the absence/presence of licensed users and to communicate without causing much interference as a secondary user network. These networks consist of two communication links for primary user detection. One link is between the primary user and the sensors, and the other link is between the sensors and the fusion center. In this study, we consider an IEEE 802.15.4a based ultra wideband (UWB) network with a noncoherent receiver structure for the first link. For the second link binary pulse position modulation is implemented to convey primary user information to the fusion center. Numerical expressions for probabilities of false alarm and detection for the overall system are obtained and validated by simulations, where the performance of the system improves with number of sensors and the reliability of the first link. The results obtained from this study can be used for improving the primary user detection performance of UWB based wireless sensor networks in noncoherent operation mode.
I. INTRODUCTION
With the growing demand on wireless communication sys-tems, challenges of the usage of limited resources increase at a tremendous rate. Energy efficiency, spectrum efficiency, interference management and reliability are some of the most important challenges in wireless communication systems [1]. Wireless Sensor Networks (WSNs) are mostly preferred for their energy efficiency even under low signal-to-noise ratios. Although unreliable communication channels may cause sig-nificantly high bit error rates, this problem can be solved using some robust approaches or technologies [2]. In WSNs, fusion center structures and the decision mechanisms are the most important factors that affect the overall system performance [3]. In [4], decision mechanisms are presented in orthogonal multiple access channels. In addition to decision mechanisms, optimum fusion rules have been investigated under some assumptions such as conditional independence [5], [6].
Another important issue for the WSNs is the coexistence of a secondary network with a primary user or a network. As an underlaying secondary system, ultra wideband (UWB) systems have been proposed [7], which are preferred in many applications due to their low complexity, low cost and high robustness to interference. UWB systems achieve robustness to interference by spreading their transmit spectrum above
500 MHz. On the other hand, despite being underlay systems many regulatory agencies require UWB systems to detect the presence of a primary user in order not to cause interference. The reliability in assessing the primary user’s activity (i.e., being active or passive) may be enhanced using multiple UWB systems in a WSN. In [8], noncoherent receivers and multiple access channel related scenarios are investigated for power consumption under Rician and Rayleigh fading channels in WSNs. In [9], distributed detection in UWB based WSNs is studied including the energy budget and the effect of bandwidth under frequency selective channels. In [10], the effects of binary pulse position modulation (BPPM) and BPPM/binary phase shift keying (BPPM/BPSK) on a UWB based WSNs are investigated for primary user detection through simulation studies, where each user transmits through orthogonal channels.
In this paper, unlike earlier UWB based primary user (PU) detection studies, standardized IEEE 802.15.4a based UWB systems [11] are considered to detect the absence/presence of the PUs with a noncoherent receiver and a BPPM transmitter structure, to provide realistic detection results. The PU activity information is assessed by the noncoherent structure of each sensor, where the local decisions are transmitted to the fusion center. In the proposed model, the fusion center does not require any complex fusion rule as each sensor transmits simultaneously its decision using BPPM either in the first or the second half of the symbol duration. Therefore, such a noncoherent receiver structure at the fusion center deciding the PU activity directly on the received signal energy decreases the energy consumption and computational complexity signifi-cantly. Numerical expressions are obtained for the probabilities of false alarm and misdetection for the overall system, and the detection performance is investigated for various link reliabil-ity cases and different number of sensors. The probabilities of false alarm and misdetection expressions are accurate and confirmed by simulations for various scenarios.
The paper is organized as follows. In Section II, system model is explained in detail for the primary user-sensor link, sensor-fusion center link and the decision rule. In Section III, the proposed system is analyzed and expressions are obtained for probabilities of false alarm and detection for the overall
system. In Section IV, both simulation and analytical results are presented for different number of sensors and various reliability of the links, confirming the validity of the analysis. In Section V, concluding remarks are given.
II. SYSTEMMODEL
The proposed primary user detection structure consists of two cascade links; between licensed user-sensors and sensors-fusion center, as seen in Fig. 1. Sensors observe the primary user’s activity, make local decisions and then transmit their binary decisions (representing absence and presence) to the fusion center using BPPM signalling. As in [12], sensors listen to either uplink or downlink of the primary system simultaneously to decide on the activity of primary user in that specific band. In the first link, the absence/presence informa-tion is decided at each sensor and the detecinforma-tion performance is explained with respect to the two hypotheses, which are given in Section II-A. In the second link, the local active or passive decisions are transmitted individually by UWB systems using BPPM signalling to the fusion center that has a noncoherent receiver structure and a decision is reached at the fusion center, which are explained in Section II-B.
Sensor-1 BPPM BPPM BPPM ˆ d(1) ˆ d(2) 1st Link 2nd Link ˜ d Fusion Center r C H A N N E L + ˆ d(K ) Sensor-K Sensor-2 Primary User d . . . . . . . . .
Fig. 1. A UWB based WSN system with noncoherent receiver structure A. Primary User - Sensor Link Structure
In the first link, each sensor decides individually on the absence/presence of the primary user. The absence or the presence of the primary user is represented by two hypotheses, H0 and H1, respectively as
H0: rf(t) = n(t) (1)
H1: rf(t) = A ejθw(t − τ) + n(t). (2)
Here, rf(t) represents the received signal in the first link,
τ is the timing offset between the two systems, w(t) is the primary user signal with amplitude A and phase θ uniformly distributed over[0, 2π), n(t) is the additive white Gaussian noise (AWGN) with variance σ2
n = N0W , where W and
N0 are the transmission bandwidth and noise power spectral
density, respectively.
The decision variable for the system is obtained as d =
2 N0
T
0 |rf(t)|2dt, where T is the integration time for the
system and | · | is the absolute value operator. The UWB receiver at each sensor compares the decision variable d to a pre-selected threshold value λ in order to take an action. Assuming the sensors are identical and the signal-to-noise
ratios (SNRs) are similar, the same threshold value is used at each sensor. Accordingly, by adjusting the threshold value, λ, the performance measures, probability of false alarm and probability of detection, for each identical system can be expressed as
Pf = Pr[d > λ|H0] (3)
Pd = Pr[d > λ|H1], (4)
respectively. When the primary system is active, the decision variable d has a central χ2-distribution1 with N = 2T W
degrees of freedom (DOF) and variance σ2 = γ + 1, where
γ = A2σs2
N0W is the SNR, σ2s is the variance of the primary
signal samples, and the additional term “1” corresponds to the normalized noise samples. When the primary system is inactive, the variance becomes σ2= 1. Thus, the probability
density function (pdf) of d for either hypothesis can be expressed as fD(d) = 1 σN2N/2Γ(N/2)d N/2−1e−d/2σ2 , (5)
where Γ(a, b) = b∞e−tta−1dt is the upper incomplete
Gamma function and Γ(a) = Γ(a, 0) is the Gamma function [13]. Based on (5) both probabilities, Pf and Pd, for each
sensor can be obtained as Px= Q N 2 , λ 2σ2 = Γ N 2,2σλ2 ΓN 2 (6)
with the corresponding σ2 values for H
0 and H1, where x ∈
{f, d} and Q(a, b) is the regularized upper incomplete Gamma function [13]. At each sensor, independent decisions ˆd(k) ∈ {0, 1} for k = {1, 2, . . . K} can be reached where ˆd(k) = 0 implies the decision “absent” and ˆd(k)= 1 implies the decision “present” for a primary user.
B. Sensor-Fusion Center Link Structure
From each sensor, one-bit local decisions{ ˆd(k)} are trans-mitted with BPPM to the fusion center through the second link. BPPM uses a signal with a constant amplitude and constant width, and positions the primary user signal information on a related position based on the local decision. Assuming all sensors transmit synchronously, the BPPM received signal can be expressed as r(t) = K k=1 s(k)(t) ∗ h(k)(t) + n(t), (7) where s(k)(t) is the transmitted symbol of the kthsensor
con-taining the estimated binary ˆd(k)information (absent/present) and is represented as s(k)(t) = p t − ˆd(k)T2s (8)
with Ts being the duration of the received signal. h(k)(t)
represents kth sensor’s channel as given in [14]
h(k)(t) =
N
n=1
h(k)n δ(t − nTp), (9)
where Tp is the channel resolution and the pulse duration,
and N is the number of multipath coefficients. To pre-vent inter-symbol interference, it is assumed that NTp ≤
Ts/2. The channel coefficients of the kth user are h(k) =
[h(k)1 h(k)2 ...h(k)N ]T, where N is the length of discrete-time
equivalent channel. In practice, the double exponential decay model is used for the modeling of UWB channels, how-ever, obtaining performance expressions in such channels are not trivial mathematically. For mathematical tractability, the Gaussian approximation model is used in this study as in [14]. Accordingly, each channel coefficient is assumed to be Gaussian distributed with h(k)n ∼ N(0, σ2h) and the users’
channels are independent and identically distributed.
To make a final decision, the instantaneous received energies of both positions are calculated and the accumulated energies are compared with each other. The position which has the maximum energy value is determined as the decision of the primary user’s activity. In most conventional systems, it is assumed that each sensor’s decision is assessed individually and the local decisions are processed with the majority rule to reach a final decision on the PU activity. In this study, assum-ing synchronous transmission of sensors, one-symbol duration is adequate to decide on the PU activity. The instantaneous received energy, ym, which is the normalized signal energy
by the noise power spectral density can be obtained for both positions m = {0, 1} as ym= 2 N0 (m+1)Ts 2 mTs2 |r(t)|2dt. (10) Comparing energy values y0 and y1, a decision on PU
activity will be reached at the fusion center. Accordingly, if y1
is larger than y0, a decision that PU is active, will be given.
Therefore, the probabilities of false alarm and detection of the overall system can be expressed as
PF = Pr[´y < 0 | H0]
PD= Pr[´y < 0 | H1] (11)
where ´y = y0− y1. The probabilities of detection and false
alarm of the overall system will depend on the qualities of both links and number of sensors. This will be discussed in the Results section. Next, system analysis of the proposed PU detection approach is presented.
III. SYSTEMANALYSIS
For analysis purposes, the discrete-time equivalent model to compute instantaneous received energy, ym, can be written as
ym= 2
N0r T
mrm, (12)
where the 2N × 1 received vector r is the concatenation of N × 1 vectors r0 and r1, r= [r0r1], given as
rm= Sh + n, m = {0, 1}, (13)
where SR∈(N ×N ) is an N × N scalar matrix representing
time-shifted pulses and h represents the combined effective channel and pulse position information for all K users. Since the elements of both h and n are Gaussian distributed, each element of rm is zero mean and has a variance of
σr20 = σh2(K − i) + σn2K for m = 0 (i.e., position “0”)
and σ2
r1 = σ2hi + σn2K for m = 1 (i.e., position “1”),
respectively. Here, i and (K − i) represent the number of sensors transmitting the binary information “1” and “0”, respectively. Therefore, the variable ym for positions m = 0
and m = 1 depending on i can be modelled with central χ2
-distribution with N degrees of freedom as in [15] and [16] by using (5) as fY0,i(y) = y N/2−1e−y/2{σ2 h(K−i)+σ2nK} {σ2 h(K − i) + σ2nK}N/22N/2Γ(N/2) (14) fY1,i(y) = y N/2−1e−y/2{σ2hi+σ2nK} {σ2 hi + σ2nK}N/22N/2Γ(N/2) . (15)
In classical approach, a predefined threshold value is chosen and a final decision is given by comparing the collected energy with this threshold [15], [16]. Therefore, obtaining an effective threshold is an important factor which affects directly the performance of the system. Different from these studies, the comparison of the collected energies for the two positions can be simply used to make a PU activity decision in this study. The probability of active decision (i.e., PU is active) can be calculated by using the distributions related to each position depending on i. Accordingly, pdf of ´y = y0− y1
can be calculated as the convolution of two pdfs. Hence, the probability of active decision can be calculated depending on i as Pact,i= 0 −∞ ∞ −∞
fy0,i(v)fy1,i((´y + v))dvd´y. (16) In Fig. 2, the pdf of ´y and the calculation of the probability of active decision are illustrated for K = 3 and i = 0 when SN R = 0 dB. Note that (16) and the simulation of the second link depending on i are in well correspondence.
For the overall detection performance of the system, the number of active decisions, i, in the first link is also im-portant. The probabilities of active decisions of the first link conditioned on hypotheses are obtained as [16]
P (i|H0) = K i Pi f(1 − Pf)(K−i) P (i|H1) = K i Pi d(1 − Pd)(K−i) (17) where i is the number of active decisions of K sensors. Ac-cordingly, the probability of deciding “active” for the overall
y' -50 0 50 100 150 200 250 300 fy' (y') 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 simulation analytical P act,0 = Pr[y'<0]
Fig. 2. Pdf of ´y for K = 3 and i = 0 when SNR = 0 dB.
system can be obtained by using (16) and (17) considering all i cases as
PF =
K
i=0Pact,iP (i|H0)
PD=
K
i=0Pact,iP (i|H1)
(18) In addition to PF and PD, a converged value is obtained
for the overall system performance when the second link is assumed as noise-free2 and can be written as
PXconv = K i=K+1/2 K i Pxi(1 − Px)(K−i)+ Feo (19)
where X ∈ {F, D}, x ∈ {f, d}, . is the ceiling operator, and Feo represents a factor that depends on even/odd situation
of K defined as Feo = ⎧ ⎨ ⎩ 1 2 K K/2 PxK/2(1 − Px)(K/2), if K : even 0 , if K : odd. (20) IV. RESULTS
In this section, the theoretical results are verified by simu-lations for different scenarios. The detection performance of a UWB sensor network with BPPM signalling is investigated under various first link situations, number of sensors, and reliability of the second link when the channel length is assumed as N = 20. The overall probability of false alarm, PF, and probability of misdetection, PMD = 1 − PD, are
obtained by considering (11) and (18). The primary user is assumed to have only an uplink channel. K sensors listen to the licensed user and decide on the activity of the PU by using Neyman-Pearson (NP) test as in [12]. These binary decisions are transmitted by BPPM to the fusion center through the second link. The fusion center reaches an overall decision.
In Fig. 3, probability of false alarm of the overall system, PF, is illustrated for various number of sensors under different
SNRs of the second link. The probability of false alarm of the
2Although the second link is assumed to be noise-free, multipath channel still affects the signal components.
first link, Pf, is 0.01. PF reaches an error floor when different
number of sensors listen to the spectrum of the primary user as SNR increases. The error floors for different number of sensors can be calculated as in (19). The lowest PF for
1-sensor system converges to Pfas SNR increases in the second
link. In addition, the performance of the system improves compared to the first link as the number of sensors in the system increases. The error floors can be reached between [0, 10] dB SNR depending on number of sensors as seen in Fig. 3. Also, it should be noted that theoretical and simulation results match well.
SNR (dB) -30 -20 -10 0 10 20 30 PF 10-6 10-5 10-4 10-3 10-2 10-1 100 Theoretical Simulation 1-sensor 3-sensors 7-sensors 5-sensors
Fig. 3. Probability of false alarm (PF) of the overall system when 1st Link’s Pf is 0.01 for 1,3,5, and 7 number of sensors
PF 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 PMD 10-4 10-3 10-2 10-1 100 Pf=0.9 Pf=0.3 SNR increasing -30 dB (0.2161, 0.002448) SNR increasing (0.9719, 0.00038) (1e-006, 0.3212) SNR increasing Pf=0.001
Fig. 4. Probability of misdetection (PMD) and false alarm (PF) of the overall system for variousPf of the 1st Link
The trade-off between the probability of misdetection, PMD, and false alarm, PF, of the overall system is shown for
different first channel reliability conditions in Fig. 4. Primary user’s channel is assumed to have an SNR of5 dB. The per-formance of the overall system is assessed for three different reliability conditions of the first link, Pf = {0.001, 0.3, 0.9},
resulting in Pmd = {0.3784, 0.0287, 0.0009}. It is assumed
performed on a wide range of SNR values[−30, 30] dB for the second link. When SNR = −30 dB, the second link is very unreliable so all cases converge to 50% probability of false alarm and misdetection as expected. When SNR = 30 dB, the second link is almost noiseless so PF and PMD converge
to probability values which are also confirmed by (19). An observation regarding(PF, PMD)-pairs should be elaborated
on. When the first link Pf is high, while PF becomes worse,
PMD much improves. While this will be to the advantage of
the PU, the secondary users in the network will not be able to communicate efficiently. On the other hand, if Pf is low, then
the PU will be interfered more often in the overall system. Therefore, a better trade-off may be when Pf is neither high
nor low (e.g., Pf = 0.3).
PF 10-6 10-5 10-4 10-3 10-2 10-1 100 PMD 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 1-theo. 1 sensor 3-theo. 3 sensor 5-theo. 5 sensor 7-theo. 7 sensor 1st Link PF: 0.01 PMD: 0.221 PF: 3e-006 PMD: 0.05672 PF: 0.00031 PMD: 0.1265 PF: 3e-005 PMD: 0.07959
Fig. 5. Probability of misdetection (PMD) and false alarm (PF) of the overall system when thePf of 1st link is 0.01 for 1,3,5, and 7 sensors
Finally, Fig. 5 illustrates the overall performance improve-ment when the number of sensors is increased. All results in Fig. 5 are obtained in a wide SNR range of[−30, 30] dB while assuming Pf= 0.01. The rate of improvement in reducing PF
is much better compared to reducing PMD when the number
of sensors is increased. For a high Pf value in the first link,
the rate of improvement would follow an opposite trend. In the figure, all numerical results are confirmed by simulations including the converged (PF, PMD) values. All in all, the
improved detection performance can be calculated for various number of sensors in the proposed noncoherent UWB sensor network system.
V. CONCLUSION
In this study, the PU detection performance of a noncoherent UWB system is studied considering PU-sensor and sensor-fusion center links. The UWB WSN system performs detection with different number of sensors and the local decisions are transmitted to the fusion center synchronously. It is shown that the analytical and simulation results match well and the information coming from the first link has a significant effect on the overall performance. Furthermore, as expected the performance of the overall system is improved by increasing
the number of sensors. The results obtained in this study can be used for improving the primary user detection performance of the UWB based wireless sensor networks in noncoherent operation mode.
ACKNOWLEDGMENT
This research was supported by 7th European Community Framework Programme-Marie Curie International Reintegra-tion Grant and TUBITAK 2211-NaReintegra-tional Scholarship Pro-gramme for PhD Students.
REFERENCES
[1] A. Osseiran, V. Braun, T. Hidekazu, P. Marsch, H. Schotten, H. Tullberg, M. A. Uusitalo, and M. Schellman, “The foundation of the mobile and wireless communications system for 2020 and beyond: Challenges, enablers and technology solutions,” in IEEE Veh. Tech. Conf. (VTC), June 2013, pp. 1–5.
[2] B. Liu and B. Chen, “Channel-optimized quantizers for decentralized detection in sensor networks,” IEEE Trans. Info. Theory, vol. 52, no. 7, pp. 3349–3358, July 2006.
[3] R. Jiang and B. Chen, “Fusion of censored decisions in wireless sensor networks,” IEEE Trans. Wireless Commun., vol. 4, no. 6, pp. 2668–2673, Nov. 2005.
[4] K. Liu and A. Sayeed, “Type-based decentralized detection in wireless sensor networks,” IEEE Trans. Signal Process., vol. 55, no. 5, pp. 1899– 1910, May 2007.
[5] P. K. Varshney, Distributed Detection and Data Fusion, 1st ed. Secau-cus, NJ, USA: Springer-Verlag New York, Inc., 1996.
[6] Z. Chair and P. Varshney, “Optimal data fusion in multiple sensor detection systems,” IEEE Trans. Aerospace and Electr. Syst., vol. AES-22, no. 1, pp. 98–101, Jan. 1986.
[7] M. Win and R. Scholtz, “Ultra-wide bandwidth time-hopping spread-spectrum impulse radio for wireless multiple-access communications,” IEEE Trans. Commun., vol. 48, no. 4, pp. 679–689, Apr. 2000. [8] F. Li, J. Evans, and S. Dey, “Decision fusion over noncoherent fading
multiaccess channels,” IEEE Trans. Signal Process., vol. 59, no. 9, pp. 4367–4380, Sept. 2011.
[9] I. Oppermann, L. Stoica, A. Rabbachin, Z. Shelby, and J. Haapola, “UWB wireless sensor networks: UWEN - a practical example,” IEEE Commun. Mag., vol. 42, no. 12, pp. S27–S32, Dec. 2004.
[10] Y. Sabucu and S. Erkucuk, “Primary user detection in IEEE 802.15.4a based wireless sensor networks,” in Signal Process. and Commun. App. Conf. (SIU),, Apr. 2013, pp. 1–4.
[11] “IEEE standard for information technology - telecommunications and information exchange between systems - local and metropolitan area networks - specific requirement part 15.4: Wireless medium access control (MAC) and physical layer (PHY) specifications for low-rate wireless personal area networks (WPANS),” IEEE Std 802.15.4a-2007 (Amendment to IEEE Std 802.15.4-2006), pp. 1–203, 2007.
[12] S. Erkucuk, L. Lampe, and R. Schober, “Analysis of interference sensing for DAA UWB-IR systems,” in IEEE Intl. Conf. Ultra-Wideband, (ICUWB), vol. 3, Sept. 2008, pp. 17–20.
[13] M. Abramowitz and I. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables, ser. Applied mathe-matics series. Dover Publications, 1964.
[14] K. Bai and C. Tepedelenlioglu, “Distributed detection in UWB wireless sensor networks,” IEEE Trans. Signal Process., vol. 58, no. 2, pp. 804– 813, Feb. 2010.
[15] S. Erkucuk, L. Lampe, and R. Schober, “Joint detection of primary systems using UWB impulse radios,” IEEE Trans. Wireless Comm., vol. 10, no. 2, pp. 419–424, Feb. 2011.
[16] S. Yiu and R. Schober, “Nonorthogonal transmission and noncoherent fusion of censored decisions,” IEEE Trans. Veh. Tech., vol. 58, no. 1, pp. 263–273, Jan. 2009.
